(a) Assignment of cases for hearing by the Supreme Court shall be made by the chief clerk of the Supreme Court, under the direction of the Chief Justice or an associate judge designated by the Chief Justice.
(b) Assignments of cases for hearing by the Appellate Court shall be made by the chief clerk of the Appellate Court, under the direction of the Chief Judge or an Appellate Court judge designated by the Chief Judge.
(c) Assignments shall ordinarily be made in the order in which cases stand upon the docket of cases ready to be heard; but counsel may, in writing and in the manner provided by the rules of the Supreme Court or Appellate Court, as the case may be, request a variation in such order. Assignments shall be made, so far as reasonably possible, in accordance with any such request or in a way which suits the convenience of counsel.